Theory of Fréchet cones
A smooth mapping of a smooth n-dimensional manifold L into a smooth 2n-dimensional symplectic manifold (M,ω) is called isotropic if f*ω vanishes. In the last ten years, the local theory of singularities of isotropic mappings has been rapidly developed by Arnol’d, Givental’ and several authors, while it seems that the global theory of their singularities has not been well studied except for the work of Givental’ [G1] in the case of dimension 2 (cf. [A], [Au], [I2], [I-O]). In the present paper,...
Applying a nonsmooth version of a three critical points theorem of Ricceri, we prove the existence of three periodic solutions for an ordinary differential inclusion depending on two parameters.
The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form in Ω, on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...